How do I cut off excess overlap of two objects?
A practical way to do this is:


Go into an orthogonal view looking down the edge of your plane roof
In Edit Mode, Put (CtrlR) 2 edge loops around your log
Slide (GG) each of your edge loops until they coincide with the slope, top and bottom.
With the knife tool, cut through (KZ) from the top vertex of the left loop to the bottom vertex of the right loop.
Rip (V)the newly created sloping edge loop.
Select linked (hover L) on the left side of the new loop, and delete faces.
Dissolve your guide loop, if you like.




But you're still in trouble: If your roof is a simple plane, either the logs will show through, or there will be a gap on the outside, or you will have coincident geometry, which will cause artifacts. So really, your roof should have some thickness, and the ends of the logs should be concealed inside it.